The Asteroid Destruction Scene in
"Rise"[VOY]

We blow up asteroids, too . . . and ours are bigger. The
following is based on a downloaded DivX vidcap of the episode, with a
framerate of 15 fps.

In "Rise", Voyager comes to the aid of the Nisu. One of their colonies
is being subjected to an asteroid bombardment. Their own attempts to
vaporize the asteroids keep failing . . . fragments still impact against
the surface. As the episode begins, we see a large asteroid tumbling
toward the planet.

The asteroid

Transcript follows:

Janeway: "Fire."

Asteroid hit by one photon torpedo, 42 seconds into the
episode

Tuvok: "The asteroid is fragmenting. But, most of the debris is still
on a collision course with the planet."
Janeway: "Target the fragments. Destroy them."
Chakotay: "That asteroid should have been vaporized. What happened?"
Kim: "I'm not sure. Sensors showed a simple nickel-iron composition. We
shouldn't be seeing fragments more than a centimeter in diameter."
(Sklar tells of the similar outcome of their own efforts on previous
asteroids.)
Tuvok: "I've destroyed most of the debris, Captain. However, targeting
scanners were unable to track two of the fragments. They have already
entered the upper atmosphere.
(Tuvok's report comes at 1:10 in the
episode, 28 seconds after the
asteroid was first hit, and 20 seconds after Janeway's order to destroy
the fragments.)

Four minutes into the episode, we learn something interesting from a
Nisu scientist named Vadum, "our most prominent astrophysicist," as per
the Ambassador's statements.

Vadum: "Ambassador, I've been analyzing the debris, and I've
discovered disturbing evidence that the asteroids are not what they seem!
They are composed of artificial materials. I must meet with you immediately
. . ." (garbling, then transmission cuts out)

A few minutes later, we learn what he means, as Torres and Chakotay
examine one of the fragments, with the Nisu Ambassador looking on.

Torres: "I've completed the mineralogical scans. The rock is composed
of trioxine, olivine, . . . waitaminute. I'm reading a concentration of
triatium."
Ambassador: "Triatium? Isn't that an alloy?"
Torres: "Yes."
Chakotay: "B'Elanna, give me a hand with this."
(Chakotay has used a pick to crack the outer layer. He and Torres now
pull the two pieces apart, revealing the rock's technology-innards.)
Torres: "This doesn't look like any asteroid I've ever seen, but I'll bet
it's the source of our triatium."

A control node for some sort of guidance system

It is discovered that the asteroids were part of a ruse by another race
to make the colony planet appear unsafe, leading to a Nisu evacuation.
The planet thus unoccupied, the other race could then stake a claim.
Naturally, Voyager saved the day. For our purposes,
however, the most interesting part of the episode is the asteroid
destruction in the beginning.

Obviously, to have an asteroid destruction scene in Star Trek is of
interest, given the level of interest the asteroid
destruction scene
in Return of the Jedi garners from pro-Wars and pro-Trek debaters
alike.

And so, with that history in mind, let's take a look at what we can
learn about this scene. What we want is a firepower analysis . . . what
we therefore need are details about the size of the asteroid, the
composition of the asteroid, and so on.

The Size of the Asteroid

In order to determine the size of the asteroid, we need something to
scale from. In this case, we have ourselves a lovely little photon
torpedo.

Voyager firing the torpedo

Two frames later

Torpedo travelling toward the asteroid

The torpedo, about to hit

Impact

From here, scaling the torpedo is a simple matter. For the sake of
being conservative, I will assume that Voyager's torpedo is fired in a
portward direction (i.e. toward the observer) . . . this will have the
effect of making the torpedo glow area smaller. It should be noted that
it is pretty clear from the episode that Voyager was shooting roughly
dead-ahead. However, making the torpedo appear to be smaller will have
the effect of making the asteroid seem smaller, making this a conservative
estimate.

Scaling off of Voyager's port side, and using
the torpedo as it appeared two frames after being fired, the central
glowing area of the torpedo (i.e. not including the streamers) is
approximately 10 meters in diameter. Now, I shall take the asteroid as it
appeared two frames before torpedo
impact (image below). (The image one frame before impact shows an
illumination of the asteroid surface, and I do not want my estimate thrown
off as a result). I count the torpedo as being a grand total of four
pixels wide,
with the central glowing area constituting two pixels or so of width. The
asteroid is sitting at an angle of about 45 degrees in the shot . . .
tipping it so the long axis is vertical, we have an asteroid length of 78
pixels, with a width varying between 37 and 50 pixels. I shall treat the
asteroid as if it were a rough cylinder.

If one pixel equals five meters, this gives the asteroid an
approximate length of 390 meters, with a width varying between 185 and 250
meters.

The original image

Illustration of torpedo outline and asteroid
axes

Treating the asteroid as a cylinder, and using 210 meters as a rough
width (the actual midpoint between the widths is 217.5), we arrive at an
asteroid volume of 13,508,063 m3.

The Composition of the Asteroid

Several statements about the composition are made. Ensign Kim refers
to the asteroid as having a "simple nickel-iron composition".
Vadum, on the other hand, implies that the asteroids are composed of
artificial materials. The tricorder scan performed by Torres would seem
to unite the two ideas . . . the asteroid contained olivine, a
common constituent of nickel-iron asteroids, but also contained
triatium, an artificial alloy. (I have no idea what 'trioxine', the other
mentioned substance, could be. A Google search for that word only came up
with some sort of new medicine.)

The extremely dark and mottled coloring of the asteroid is a bit odd,
but not unreasonably so. From what we know of the asteroid based on Kim's
scans, it should fall
within the parameters of an M-type . . . S-type if the olivine was common
throughout, and not simply present on the surface, for example. The
specimen collected by Voyager was obviously solid, and easy to crack.
Judging by the color and composition, though, it would not seem to be
representative of most of the asteroid. For our purposes, then, the
average Sol system asteroid density of 3,000 kg/m3 seems fair
to use here, as well.

This density, taken with the volume, gives us a total asteroid mass of
40,524,189,000 kilograms, or 40,524,189 metric tons.

In order to make this an absolute lower limit, I shall ignore the fact
that it would require more energy to vaporize a lower-density asteroid
than it would if it were solid iron, due to heat expansion and
fragmentation effects. Further, I will calculate only based on iron
(nickel has similar properties), and assume that it constitutes 60% of the
mass of the asteroid, leaving us to deal with a mere 24,314,513,400
kilograms.

In effect, I am leaving plenty of room for Harry's comment that "we
shouldn't be seeing fragments more than a centimeter in diameter" by
estimating only 60% vaporization of the asteroid. Of course, some
would argue that I should not claim any vaporization at all, but that's absurd .
. . it's a photon torpedo, not a space blender. There's no way it can dice
the asteroid into one-centimeter fragments without vaporizing the vast majority
of the asteroid, minus those little less-than-a-centimeter escapees.
(Indeed, even to assume that the remaining 40% of the asteroid would end up
diced in such a fashion stretches believability.)

If we assume that the asteroid started out at 200 Kelvin, and that it
would therefore take 7.6 megajoules to vaporize one kilogram of iron, we
are still left with a necessary energy figure of 184,790,301,840
megajoules. That's 184,790 TJ, or 44 megatons, as an absolute
I-bent-over-backward lower limit.

Now, let's take a look at the asteroid as the more
rabid of my opponents look at
theirs, so we can get something closer to an upper limit. First, the
density will have to be bumped up from 3,000 to 7,000 kg/m3.
This gives us a mass of 94,556,441,000 kilograms. Let's assume that the
iron (and/or similar nickel) constitute 90% of the asteroid's mass, or
85,100,796,900 kilograms. At 7.6 megajoules per kilogram, this works out
to 646,766,056,440 megajoules. That's almost 650,000 TJ, or 154.5
megatons. Then again, given that all this energy must be deposited
into the asteroid in a fraction of a second by an explosive device, this, too,
is probably a low-end figure.

As it happened, the asteroid was not vaporized in the episode as
everyone expected it to be, due to the fact that it wasn't exactly a normal
asteroid. Of course, this is irrelevant for our purposes since we know
what was expected, but it is interesting nevertheless. I may try to work
up some sort of acceleration parameters on the large pieces (the
biggest is ~100m) that are flung
off to the right at impressive speed (750 m/s minimum for the ~100m
fragment). Note also that the asteroid is shattering violently in the
first image, which is one frame (1/15th of a second, or .067s) after
impact.

Destruct

Five frames later

Last frame that shows the asteroid,19 frames
(1.26 seconds) after impact

Conclusions

100 megatons (420,000 terajoules) would appear to be an extreme but
fair low-end figure for this scene's photon torpedo yield. It can't really be any lower, and
is much more likely to be higher. Given other incidents of starships
versus asteroids (the moon-sized object in "This Side of Paradise"[TOS],
the wormhole scene of ST:TMP, and Dukat's efforts in "Return to
Grace"[DS9]) and planets ("Skin of Evil"[TNG]), this fits in well. The
Motion Picture actually could be used to provide a higher yield, given
that the torpedo disappears completely from our view (implying a larger
asteroid), but that example becomes an odd one to use, due to the wormhole
and any unexpected effects it might have.

Rabid Warsies will undoubtedly sneer at the 100 megaton
figure. However, their own high-end estimates of the highest turbolaser firepower seen in the canon
(Mike Wong's 250 TJ and 1500
TJ figures, as well as another person's 701 to 2863
TJ) don't
come anywhere close to even 100 megatons (420,000 TJ), much less the 200
gigatons (836,800,000 TJ) from their non-canon.

Not that I find that surprising.

Note
also that the "Rise" asteroid is not the largest asteroid we've seen destroyed by torpedoes, or
the densest. "Cost of Living"[TNG] shows the Enterprise-D
using two torpedoes to destroy an asteroid, and the first torpedo is not even
visible for most of the second torpedo's trip.

Second torpedo close-by at upper left, first torpedo
barely visible at upper left of asteroid.

First torpedo long since vanished, second torpedo still en route

Both torpedoes no longer visible

Results:

This asteroid is shattered, not vaporized. The asteroid was large enough, however, to have a
differentiated core composed of "densely compressed nitrium and chrondite", and the remaining core was
of sufficient size and density to cause planetwide damage to the planet below.
Even if we merely assume a 10-15 megaton blast similar to Tunguska,
that's still an asteroid of tremendous size, tremendous density, or both (at
somewhat less tremendous levels). Data concluded that
another torpedo would be unlikely to damage the core, but was able to shatter the core with
a technobabble particle beam from the deflector. Judging by the beam, the
core remnant was the size of the secondary hull of the Enterprise. The remaining core fragments no longer posed a danger, and were then flown through by the Enterprise on her way
out of the system:

Fragments of the asteroid's core, with Enterprise-D for scale

Objections

1.If Chakotay was able to tap a piece of the asteroid open
with a little pick-axe, the asteroid must have been brittle. If it was
made of such brittle materials, Voyager's torpedo should have done more
damage.

There's a profound difference between taking a sharp pick against a
solid rock and vaporizing it with a photon torpedo explosion. First, a
rock has characteristics such as cleavage
and fracture. That is, in fact, one of the ways rocks are identified.

Torres identifies olivine as one of
the substances in the rock. You'll note that olivine has a brittle,
conchoidal (shell-like) fracture. In other words, it breaks easily into
curved fragments, not unlike glass does. Also pay attention to the fact
that it is rather hard, but with a low density. Something hard, low
density, and brittle is going to be easy to crack.

Compare this with iron, which they
thought the asteroid was made of. It's softer,
and thus more malleable. It has a higher density, and a jagged, torn
fracture. Now, let's say you fire a bullet at a wall made of olivine.
You'll probably end up with a hunk of broken fragments flying away, and
might even get cracks running from the point of impact. Do the same to an
iron wall, and if the bullet penetrates more than a dent's worth, you'll
get torn metal.

Detonate a thermonuclear weapon next to that wall, and the olivine wall
will probably shatter. The more resilient iron wall may either tear wide
open, or just sit there and melt, et cetera, depending on various factors.

This would assume, of course, that the entire asteroid was olivine, and
not nickel-iron with a couple of oddball chunks of olivine. Given the fact
that it fragmented in the way it did without vaporizing as expected, that
isn't a bad hypothesis. But, then, the Nisu astrophysicist dude mentioned
in his transmission that the asteroids were composed of artificial
materials . . . whether he had simply found evidence that triatium
alloy was part of the asteroid, or had found that sensor signals were
being distorted, or found that the majority of the asteroids were
literally artificial is not clear.

In any event, the brittleness of a material is no indication that it
will be easier to vaporize . . . indeed, it is far more likely to fracture
uncontrollably, and in this case unexpectedly.

2.Voyager didn't actually destroy the asteroid, therefore
you can't claim firepower off of this episode.

Why not? The crew fully believed that they had an iron-nickel asteroid
before them, and that it could be vaporized by photon torpedo. The fact
that it wasn't vaporized does not negate their belief that they could
have done so. Further, a 100m chunk and a smaller, perhaps 50 meter
chunk flew toward the planet. Another chunk of about 40 meters flew off to
the left. There was also a bunch of other crap flying around, but it's too
small (and the vidcap is too low-res) for me to get much
more out of it. Let's say, for the sake of argument, that an extra 50m
asteroid's worth of material made it out of the torpedo blast.

If all that is correct, then it means 688,410 m3 of debris
was left over by the torpedo blast. For an asteroid that started out at 13,500,000
m3, that ain't half bad, given the unexpected nature of what
occurred.

3.Hey, I saw those two pieces
flying off to the right, and when they hit the planet they weren't nearly that
big.

I disagree. First, you're
assuming that Tuvok is stupid, and would not have tried to take out the largest
pieces headed toward the planet first. Second, and more importantly,
those two pieces that depart the asteroid are flying away from one another at a
30-45 degree angle. The chances of them magically coming back together to
become the two pieces that hit within kilometers of one another are staggering,
to say the least. It would basically have to be a Q-inspired
trajectory.

4. You scaled the asteroid
wrong. First, torpedo glow doesn't increase after the torpedo exits the
launcher. Second, you scaled the torpedo when it was at the greatest
distance from the launch point, and you can't know how big the asteroid is from
that.

The scaling is correct, within a
reasonable margin of error. First, torpedo glow does
indeed increase . . . it's a
shield after all, and we can't assume it's raised to
full strength the nanosecond the torpedo exits the tube.

In regards to the notion that I should've scaled the torpedo off of an earlier
pic, let's take a look, using the "Hutt" methodology:

The pic I used for scaling:

The one
they think I should have used:

The frame of the
asteroid and torpedo used for scaling

A
comparison image:

In the last pic above, there are two small squares and an itty-bitty
square. The top-most two are, from the left, the frame they think I should
have used, and the frame I did in fact use to scale the torpedo.
Both have been reduced in size so that all the torpedoes are all the same
size. Below the left frame, you can see a perspective-free schematic
drawing of the 130-meter-wide Voyager, roughly (and conservatively) scaled to
the navigational deflector of the scene above it. The width of the ship is
22 pixels . . . the length of the asteroid is (still) 78 pixels. Though
the margin for error is greater using this method (especially given the small
number of pixels we're dealing with), we still come up with a figure of 460
meters, 70 meters more than my figure. It would be even larger with a less
conservatively-scaled schematic view. And, if torpedoes do not in
fact seem to increase in size, and if we used the itty-bitty frame on the right
for scaling, we'd end up with an asteroid a kilometer in length . . . and
remember, the firepower would scale with the volume. Thus, we could quite
easily end up beyond the 500 megaton "Skin of Evil"[TNG] territory, up
into the 1.4 gigaton range.

So, what do you say we leave the scaling alone,
and keep the conservative 100 megaton figure?

(After all, the
"photonic torpedoes" deployed on Earth Starfleet ships in the early
2150's were capable of putting "a three kilometer crater into an
asteroid"(Reed, "The Expanse"[ENT2]). Estimates of the
yield from this example vary between 20 and 40 megatons, but either is more than
sufficient to allow us to grant 100 megaton warheads 220 years later.)

And besides, given
the torpedo's travel to the asteroid, the scaling I've used has to be accurate.
First, let's look at the torpedo two frames after departing the launcher (at
15fps):

Now, let's look at it a full two frames later:

Thirteen frames later (after we see the asteroid alone for a
bit), the torpedo comes into view at this point:

One single frame later, the torpedo reaches this point:

Six frames later:

Now, it takes an additional 11-12 frames after the above frame
for the torpedo to hit the asteroid, depending on whether one wishes to call the
impact the first of the below frames, or the second:

Now, would someone please explain to me how that could be an
itty bitty non-Voyager-size asteroid, given the torpedo travel time? Even
if you assume that Voyager fired the torpedo in a direction so that it would've
grazed the 'camera', the thing still had to have travelled about 100 meters
within four frames. And then, it still took 32-33 additional frames
for the torpedo to reach the asteroid. Even if we ignore the obvious
torpedo acceleration, that still implies that the torpedo has to travel a great
distance to reach the target.

How could it not be Voyager-sized?

Thanks to the peculiarly-named "Slobba the Hutt" for the
original scaled image from which my comparison above was made.

Special thanks to J.G. for providing the screencaps from
"Cost of Living"[TNG]